Lattice QCD input for axion cosmology

Abstract

One intriguing BSM particle is the QCD axion, which could simultaneously provide a solution to the Strong CP problem and account for some, if not all, of the dark matter density in the universe. This particle is a pNGB of the conjectured Peccei-Quinn (PQ) symmetry of the Standard Model. Its mass and interactions are suppressed by a heavy symmetry breaking scale, fa, whose value is roughly greater than 109 GeV (or, conversely, the axion mass, ma, is roughly less than 104 μ\texteV). The density of axions in the universe, which cannot exceed the relic dark matter density and is a quantity of great interest in axion experiments like ADMX, is a result of the early-universe interplay between cosmological evolution and the axion mass as a function of temperature. The latter quantity is proportional to the second derivative of the QCD free energy with respect to the CP-violating phase, θ. However, this quantity is generically non-perturbative and previous calculations have only employed instanton models at the high temperatures of interest (roughly 1 GeV). In this and future works, we aim to calculate the temperature-dependent axion mass at small θ from first-principle lattice calculations, with controlled statistical and systematic errors. Once calculated, this temperature-dependent axion mass is input for the classical evolution equations of the axion density of the universe. Due to a variety of lattice systematic effects at the very high temperatures required, we perform a calculation of the leading small-θ cumulant of the theta vacua on large volume lattices for SU(3) Yang-Mills with high statistics as a first proof of concept, before attempting a full QCD calculation in the future. From these pure glue results, the misalignment mechanism yields the axion mass bound ma(14.6±0.1) μ\texteV when PQ-breaking occurs after inflation.

Publication
Physical Review D
Enrico Rinaldi
Enrico Rinaldi
Research Scientist

My research interests include artificial intelligence and quantum computing applied to particle physics and quantum many-body systems.

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